From my understanding of the article, I think the headline is a little misleading. The N=4 super Yang-Mills theory sounds like it is right if you look at the world in just the right way and ignore some (even) more complicated bits and that you work out a solution in that simplified set of conditions to help work out solutions in the more general case. Am I wrong?

It resembles the sociological discussions you sometimes see in science fiction: If you transplant a problem to a setting with well-defined rules and properties of your choosing, it might be possible to get a better understanding of the interesting parts of it - even if the setting is clearly removed from this world.

On the software side, there's also a resemblance to testing: Given this setting I just created, which has a tenuous resemblance to real life, how does this bit of code respond to assorted prodding?

It would be more accurate to say that what you are studying is not even wrong!

Yeah, that rather misses the point of that excellent quote.

The point is that when doing work in this mathematical space you can make testable predictions about that space and explore its properties. Hence you can very much work on this and define whether something is right or wrong even if it might not apply to what occurs in the real world.

Now that this out of the way, why should anyone be surprised that you might study at length things that are less than the complete truth ?

After all, we know that euclidean geometry is not an accurate representation of the real world and yet we all start with it (and many of us stops there).

Euclidean geometry is not a theory in physics, so maybe it isn't the best comparison. Lets instead say Newtonian mechanics. Newtonian Mechanics is not "true" in the sense that it doesn't generate correct results in all regimes. However in the "not too small, not too big, not too fast" regime it produces very accurate results. It was and still is a good theory. General Relativity is a better one.

N=4 super Yang-Mills does not produce accurate real world results in any regime. Its results are completely unphysical, and we've known since the start that it was unphysical. That is what makes this sort of study a little more surprising than studying Newtonian Mechanics. We're interested in it because of its form, not because of its results.

Theoretical physics is not math. Formally, Theoretical Physics belongs to Physics (if you study classification of different subjects at university). Theoretical computer science belongs to math (if you study classification used at universities). So, if you study theoretical physics, you are a physician. If you study theoretical computer science you are mathematician. Same with numerical analysis which belongs to math.

And it is totally right to study subjects which has no bearing in reality. Mathematicians have done this for ages. For instance, number theory has been heralded as the purest form of math, and the finest, because it has no applications in reality. Professor Hardy toasted "may number theory never find its use in real life". To solve real life problems is considered as "dirty" and any one can do that. It is easier to solve an equation, than develop a theory of equations: (when are they solvable, do they have a solution at all, etc). Pure math is finer than applied math. Physics is "dirty" and easier. Read the "Fermats last theorem" by physics PhD Simon Singh, to learn more about how physicians and mathematicians differ (physicians consider math to be "finer").

But, it turned out that number theory has lots of applications in computer science, for instance cryptography. So, what is considered as useless, might change some time later. Same here.

Theoretical physics is not math. Formally, Theoretical Physics belongs to Physics (if you study classification of different subjects at university). Theoretical computer science belongs to math (if you study classification used at universities). So, if you study theoretical physics, you are a physician. If you study theoretical computer science you are mathematician. Same with numerical analysis which belongs to math.

And it is totally right to study subjects which has no bearing in reality. Mathematicians have done this for ages. For instance, number theory has been heralded as the purest form of math, and the finest, because it has no applications in reality. Professor Hardy toasted "may number theory never find its use in real life". To solve real life problems is considered as "dirty" and any one can do that. It is easier to solve an equation, than develop a theory of equations: (when are they solvable, do they have a solution at all, etc). Pure math is finer than applied math. Physics is "dirty" and easier. Read the "Fermats last theorem" by physics PhD Simon Singh, to learn more about how physicians and mathematicians differ (physicians consider math to be "finer").

But, it turned out that number theory has lots of applications in computer science, for instance cryptography. So, what is considered as useless, might change some time later. Same here.

Not to mention that imaginary numbers have lots of applications in engineering, which is very real world.

While research on fruit flies is, to most of the scientific community, immediately recognizable as having various potential benefits to mankind, the same cannot be said of many other fields of research.

I'm going to get downvoted for this, but consider high energy physics, at least some nuances in it. Is there any conceivable way research in those areas will benefit our society in the slightest way within the next few generations? And that is my issue with fields like string theory or "pure" mathematics. Even if working on them and pouring money into them will produce rewards, they will come so far in the future that they are of negligible value to us now.

I've done physics research, although more or less engineer-related, acoustics and such. And no matter what some may think, devoting more resources towards the immediate problems of this world isn't a bad thing.

I'd say that you are a mathematician and that there's absolutely nothing wrong with that.

That's what it sounds like to me also. Maybe closer to the applied math side, but still math.

The difference between a theoretical physicist and a mathematician is pretty much what department she happens to be in at a university. I know mathematicians and physicists who study literally the exact same thing. There's also tons of overlap in publishing, with mathematicians publishing in physics journals, and theoretical physicists publishing in math journals (less of the latter than the former IME, or maybe it is just that I read more physics journals).

If the author calls himself a physicist, he's a physicist. If he called himself a mathematician, I wouldn't argue with that either. It has more to do with what classes he took and what degrees he got than what he is actually researching.

While research on fruit flies is, to most of the scientific community, immediately recognizable as having various potential benefits to mankind, the same cannot be said of many other fields of research.

I'm going to get downvoted for this, but consider high energy physics, at least some nuances in it. Is there any conceivable way research in those areas will benefit our society in the slightest way within the next few generations? And that is my issue with fields like string theory or "pure" mathematics. Even if working on them and pouring money into them will produce rewards, they will come so far in the future that they are of negligible value to us now.

I've done physics research, although more or less engineer-related, acoustics and such. And no matter what some may think, devoting more resources towards the immediate problems of this world isn't a bad thing.

Well, if you postpone research because it will only have results far into the future, you will never reach those results.

Not to mention that imaginary numbers have lots of applications in engineering, which is very real world.

I see this a lot but it isn't quite true, or at least it is misleading.

Electrical engineering uses the complex number system because imaginary numbers form an orthogonal basis to the real number system and is less complicated to work with than full on linear algebra, not because there is any inherent physical reality to the square root of negative one.

While research on fruit flies is, to most of the scientific community, immediately recognizable as having various potential benefits to mankind, the same cannot be said of many other fields of research.

I'm going to get downvoted for this, but consider high energy physics, at least some nuances in it. Is there any conceivable way research in those areas will benefit our society in the slightest way within the next few generations? And that is my issue with fields like string theory or "pure" mathematics. Even if working on them and pouring money into them will produce rewards, they will come so far in the future that they are of negligible value to us now.

I've done physics research, although more or less engineer-related, acoustics and such. And no matter what some may think, devoting more resources towards the immediate problems of this world isn't a bad thing.

I'm going to get downvoted for this, but consider high energy physics, at least some nuances in it. Is there any conceivable way research in those areas will benefit our society in the slightest way within the next few generations? And that is my issue with fields like string theory or "pure" mathematics. Even if working on them and pouring money into them will produce rewards, they will come so far in the future that they are of negligible value to us now.

I've done physics research, although more or less engineer-related, acoustics and such. And no matter what some may think, devoting more resources towards the immediate problems of this world isn't a bad thing.

The issue is that to really benefit, you need to research ways to apply the results of research like what the LHC is currently doing. That will take some unknown amount of time. But without those first results, you don't get the secondary research that leads to actual applications.

For example, the transistor. It took decades for transistors to give us the computer. But semiconductors were being worked with as early as the 1930s, with a working transistor in the 1950s. This is direct result of quantum mechanics research by the theoretical physicists. Lasers, atomic clocks (which allow for GPS), and a few other pieces of kit are demonstrating other ways to apply quantum mechanics.

But, someone has to start somewhere, so that other researchers who are a bit more adept at thinking up applications of the results can build upon it. In a way, the amount of effort and time it took to go from early quantum mechanics to a working transistor is an even bigger reason to continue funding research where the applications are decades out. So we can actually reap the benefits decades out instead of maybe centuries.

Awesome article. Just one small remark from one PhD to another, don't be an apologist. When it comes to fundamental sciences you can't use definitions like "right", "wrong", "interesting", "important", etc. If you like it, you study it, if you don't you go your own way.

You should get downvoted, although your mention of 'engineer-related' gives me a sense of where you are coming from.

You misunderstand me. I don't believe that there is anything not worth researching, only issues with funding going to one place or another.

Also, when research related to these achievements were conducted the people involved more or less had an idea of what was going on. The Manhattan project and most of what was done between the 40s and 60s has very, very little in common with what CERN is doing today.

I studied these theories in my Masters degree. All I managed to say was that those theories are partly true. Only you don't know which part till a new theory has replaced them. Not very helpful really!

Well, if you postpone research because it will only have results far into the future, you will never reach those results.

I'm not talking about postponing anything, but thinking twice before we throw billions down into such projects. Mathematics is easy on the budget, other fields sadly aren't.

If you only throw money for short term research, soon you will hit a wall where advancement is not available anymore. You only have applied research because others have done the long term basic research necessary so the tools are available.

Take electronics as an example. Transistor research took a long time to be researched and applied (decades). By your reasoning, it shouldn't have been done, because valves were still there and could be improved by research. And the implications of the transistor are such that almost everyone in the world depends on it nowadays.

Very good article and some very nice comments. As a long time physics guy (degree and subsequent self study) the article makes complete sense. I would say you are modeling potential future mathematics describing the real world with a simpler mathematical model as a test. Sort of a model of a model, Why not?

You should get downvoted, although your mention of 'engineer-related' gives me a sense of where you are coming from.

You misunderstand me. I don't believe that there is anything not worth researching, only issues with funding going to one place or another.

Also, when research related to these achievements were conducted the people involved more or less had an idea of what was going on. The Manhattan project and most of what was done between the 40s and 60s has very, very little in common with what CERN is doing today.

With all of the government money going to things like oil subsidies, sending arms overseas, farm subsides, and countless other areas of society, I think it's a little bit short-sighted to talk about trying to distribute research funding properly 'within' science without recognizing that the actual percentage of GDP we spend on basic research is in the noise.

And no, the people doing the research back then had no idea the potential future uses of what they were studying. You're looking through the lens of hindsight, which we don't have for the current HEP program.

In biology, we generally use "model" for what you call "theory"; i.e. fruit flies are model organisms, population genetic research often uses the Wright-Fisher population model, etc.

The same is true in a number of other fields. I didn't mind the discussion on the field specific usage and definitions of "theory," but I think simply relating it to the concept of a model would have been much more succinct. I realize it's not exactly the same thing (physics has both theories and models, and they mean different things), especially in the jargon sense specific to physics, but it's also something very quickly graspable for most, and would have strongly underscored some of the advantages to studying this theory in a way many could relate to immediately.

We use simplified models all the time to describe and study real world problems whose complexity either makes them impractical or still too difficult to model fully (areas where we simply don't have a complete understanding are similar). Having a simplified model to approach these problems which does a fair job of approximating, or at least serves as a foundation for exploring potential directions to approach a solution in a more complete model, can be exceptionally important.

Thanks for the descriptors of your work. However, the political jabs aren't really neccessary.

Unfortunately for science (and especially for scientists), science and politics are joined at the hip. For as long as we are reliant on public funding, politics will in fact be something that scientists need to think about, comment on, and get involved in.

You should get downvoted, although your mention of 'engineer-related' gives me a sense of where you are coming from.

You misunderstand me. I don't believe that there is anything not worth researching, only issues with funding going to one place or another.

Also, when research related to these achievements were conducted the people involved more or less had an idea of what was going on. The Manhattan project and most of what was done between the 40s and 60s has very, very little in common with what CERN is doing today.

If it's practical, government shouldn't fund it. Governmental funding should focus on the types of issues not suited to private industry.

After all, private industry does a perfect job at everything practical so they can make money off it.

Or so the excuse goes every time we want to fund something practical that might step on someone's toes or ruin their ongoing exploitation of a situation.

It's funny how that works out. We can't fund "practical" science (unless it's a joint funding situation where a private partner will assume control of the resulting intellectual property: THAT is fine) because it might hurt someone's business, sometime, somehow, which is for some reason the public's problem rather than that business'. Yet we can't fund theoretical science because it's not practical and we're not sure we're going to "get a good enough return on our investment." Talk about wanting to eat your cake and still have it too.

I was a math major at a college that allowed physics courses to count towards math. From that perspective, it's really, really hard to distinguish between theoretical physics and applied math. At least one of the math courses I took could have easily been taught in the physics department, without raising an eyebrow.

I fundamentally object to the classification schema implied by

Quote:

I’m not a mathematician, however. I’m a physicist. I don’t study things merely because they are mathematically interesting.

By that definition, no one in applied math is a mathematician. Many applied math subjects have applications to string theory. Are all of those guys really physicists, but didn't realize it?

Furthermore, the fact that the application of the work is in string theory should give someone pause in defining themselves only as a physicist. There are plenty of mathematicians (who would define themselves only as mathematicians) poking around that theory. Frankly, there's way more interesting pure math bouncing around the field of string theory than there is real-world-describing going on in it.